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类型 基础研究 预答辩日期 2017-12-26
开始(开题)日期 2014-11-14 论文结束日期 2017-09-29
地点 中心楼2楼自动化学院会议室 论文选题来源 国家自然科学基金项目     论文字数 5.4 (万字)
题目 非线性系统多维泰勒网控制的稳定性分析及性能优化
主题词 多维泰勒网,非线性系统,稳定性分析,动态调节,性能优化
摘要 非线性是自然界和工程技术中最普遍的现象,自动控制领域一直寻求能够直接对非线性系统进行设计与处理的方法,设计一种用于非线性系统控制的高性能控制器又是一个有重大理论价值与实践意义的问题。本文立足于这一问题,从系统稳定性分析及性能优化出发,旨在从理论层面对多维泰勒网控制器在非线性系统中的应用研究提供一定的基础。 多维泰勒网控制器是在线性控制器基础上扩展的一种新型固定结构控制器,采用类似泰勒级数展开的形式对输入信号进行指定幂次的高阶扩展,从而使控制器存在良好的逼近性能。这样,控制器就具备了实时性好,结构简单易于工程实现且自身具有改进系统响应的能力。同时又可以凭借控制器的固定结构,从一定程度上弱化控制器设计对系统模型信息的依赖。针对这一情况,本文围绕多维泰勒网控制器在非线性系统中的应用问题展开研究,主要探讨了几类非线性系统使用多维泰勒网控制器时需要什么样的假设条件,控制器需要处理系统的什么信息,系统性能与控制器参数之间有着什么样的关系和控制器如何实现四个问题。全文的研究工作面向不同数学工具描述的三类四种非线性系统,同时还兼顾工程实际中出现的一些限制条件。论文的主要工作概括如下: 1. 针对具有零阶保持器的单入单出采样非线系统的跟踪控制与性能优化问题,提出了一种基于离散多维泰勒网控制器的新型控制方法。使用反馈线性化理论和Delta算子理论,证明了离散多维泰勒网控制器可以使单入单出非线性系统的输出响应渐近跟踪给定的参考信号。无需在线优化,离散多维泰勒网控制器可以使系统实现动态调节,从而达到优化闭环系统性能的目的。通过前述证明过程明确了离散多维泰勒器控制器在单入单出采样非线性系统中应用时系统应满足的假设条件,论证了系统响应与控制器参数之间的关系,给出了一个易于实现的控制器设计过程。此外,通过一个数值算例验证了离散多维泰勒网控制器用于单入单出采样非线性系统时,不仅实现了系统的渐近跟踪控制,还得到了较好的系统性能。 2. 在非线性系统存在状态时变时滞的情况下,针对单入单出非线性时变时滞系统的渐近稳定和性能优化问题,提出了一种基于多维泰勒网控制器的新型控制方法。利用增广反馈线性化方法、Lyapunov-Razumikhin定理以及多项式逼近定理,证明了多维泰勒网控制器可以镇定单入单出非线性时变时滞系统,并且无需系统在线优化便可按给定的性能指标进行动态调节,从而达到改善系统暂态响应的目的。通过证明过程明确了多维泰勒器控制器渐近镇定单入单出非线性时变时滞系统时系统应满足的假设条件,论证了系统响应与控制器参数之间的关系,给出了一个易于实现的控制器设计过程。并且通过一个工程中常见的连续搅拌反应釜(CSTR)系统和一个数值算例,验证了多维泰勒网控制器用于单入单出非线性时变时滞系统时不仅可以渐近镇定系统状态,还可以优化系统性能。 3.考虑了工程中常见的执行器饱和现象,研究了控制输入以非线性隐含的形式作用于系统的多入多出非仿射非线性系统的多维泰勒网渐近跟踪和性能优化问题,提出了一种基于多维泰勒网控制器的新型控制方法。通过构造滤波变量及其相关估计式,证明了多维泰勒网控制器可以使多入多出非仿射非线性系统实现渐近跟踪控制。通过多项式逼近定理,证明了系统无需在线优化即可通过动态调节实现改善系统暂态响应的目的。在这个证明过程中明确了多维泰勒网控制器需采用两自由度控制和系统应具备的假设条件,论证了系统响应与控制器参数之间的关系,给出了一个易于实现的控制器设计过程。通过一个两关节机械臂数值算例,验证了多维泰勒网控制器用于考虑执行器饱和的多入多出非线性系统,不仅实现了系统的渐近跟踪控制而且还得到了较理想的系统性能。 4.在前述考虑执行器饱和的非线性系统多维泰勒网跟踪控制问题和非线性时变时滞系统多维泰勒网镇定控制问题研究的基础上,研究了考虑时变时滞与非线性双重影响下的非线性时变时滞系统的跟踪控制和性能优化问题,提出了一种基于多维泰勒网控制器的新型控制方法。利用增广反馈线性化方法和Lyapunov-Razumikhin定理,借助滤波变量及其相关估计式,证明了多维泰勒网控制器可以使考虑执行器饱和的非线性时变时滞系统实现对给定信号的跟踪控制。凭借多项式逼近定理,基于多维泰勒网控制器的非线性时变时滞系统无需在线优化即可改善系统的暂态响应。在证明过程中,明确了多维泰勒网控制器需采用两自由度控制和系统应具备的假设条件,论证了系统响应与控制器参数之间的关系,给出了一个易于实现的控制器设计过程。对一个单入单出连续搅拌反应釜(CSTR)系统和两入两出非线性时变时滞系统分别进行了数值仿真,验证了多维泰勒网控制器不仅可以使前述系统实现渐近跟踪,而且还可以优化系统性能。在两入两出非线性时变时滞系统数值仿真的基础上,初步探讨了多入多出非线性时变时滞系统的多维泰勒网控制问题。
英文题目 STABILITY ANALYSIS AND PERFORMANCE OPTIMIZATION OF MULTI-DIMENSIONAL TAYLOR NETWORK CONTROL FOR NONLINEAR SYSTEMS
英文主题词 multi-dimensional Taylor network (MTN),nonlinear systems,stability analysis,dynamic regulation,performance optimization
英文摘要 Nonlinear is the most common phenomenon in nature and the engineering that the direct design method of the controller for nonlinear systems is desired eagerly in the automatic control field. So, a good performance controller for nonlinear systems is of great significance in theory and practice. Based on this problem, this thesis aims to provide a basis for the application of the multi-dimensional Taylor network (MTN) controller in nonlinear systems theoretically. MTN controller, a new fixed structured controller based on linear controller, is extended with controller inputs for high power similar as Taylor series which does well in approximation. In this way, the controller has the advantages of good real-time, easy to implement with a simple structure and the strong ability to improve the transient response. Due to the fixed structure of controller, the dependence of controller design on system model information can be weakened. In response to this situation, this thesis focuses on the application of MTN controller in nonlinear systems. It mainly studies the application of the MTN controller in nonlinear systems from four aspects: What assumptions are necessary for the system? What information of the system is needed for the controller? What is the relationship between system performance and the controller parameters? What kind of the method can be used for the controller design? The research of this thesis is oriented to above four problems of nonlinear systems with three types which described by different mathematical tools and some constraints in practice. The main contributions of this thesis can be summarized as follows: 1. For tracking control and performance optimization of single-input single-out (SISO) sampled-data nonlinear systems with zero-order holder (ZOH), a new control method based on the discrete MTN controller is proposed. Through the feedback linearization and Delta operator, the SISO nonlinear systems can track the reference by the discrete MTN controller. And the performance of the closed-loop system can be improved through dynamic regulation without of the online optimization. Assumptions for asymptotic tracking and dynamic regulation of discrete MTN controller for SISO nonlinear systems are obtained by the above proof. The relationship between system response and controller parameters is also demonstrated by the above proof. And a convenient design procedure of the discrete MTN controller is given. In addition, asymptotic tracking and performance optimization of SISO nonlinear systems are illustrated by an example. 2. Target of asymptotic stabilization and performance optimization of SISO nonlinear systems with state time-varying delay, a novel approach based on the MTN controller is proposed. By using the augmented feedback linearization, Lyapunov-Razumikhin theorem and polynomial approximation theorem, it is proved that the MTN controller can stabilize the SISO nonlinear time-varying delay systems. And the system transient is improved according to an index through dynamic regulation without of the online optimization. Assumptions for asymptotic stability and dynamic regulation of the MTN controller for SISO nonlinear systems are obtained by the above proof. The relationship between system response and controller parameters is also demonstrated by the above proof. And a convenient design procedure of the MTN controller is given. Through a continuous stirred tank reactor (CSTR) and a numerical example, the MTN controller for SISO nonlinear time-varying delay systems cannot only asymptotically stabilize the system can also optimize the performance of the system is verified. 3. Considering actuator saturation and implicit form of system input, the problem of asymptotic tracking and performance optimization of multi-input multi-output (MIMO) nonaffine nonlinear systems with the MTN controller is studied. Therefore, a new control scheme based on the MTN controller is proposed. By constructing the filter variable and its estimation, it is proved that asymptotically tracking for MIMO nonaffine nonlinear systems can be achieved by the MTN controller. Through the polynomial approximation theorem, the transient response can be enhanced by dynamic regulation without online optimization. Assumptions for asymptotic tracking and dynamic regulation of the MTN controller for MIMO nonlinear nonaffine systems with two degrees-freedom design method are obtained by the above proof. The relationship between system response and controller parameters is also demonstrated by the above proof. And a convenient design procedure of the MTN controller is given. Through a two-stage manipulator, asymptotic tracking and dynamic regulation of the MTN controller for MIMO nonlinear affine systems are showed. 4. Based on above two contents, a novel control scheme, that based on the MTN controller, is proposed to deal with the tracking control and performance optimization for nonlinear time-varying delay systems which influenced by time-varying delay and nonlinearity. By using the augmented feedback linearization and Lyapunov-Razumikhin theorem, tracking control for nonlinear time-varying systems with the MTN controller is proved through constructing the filter variable and its estimation. By the polynomial approximation theorem, the transient response can be improved by dynamic regulation without online optimization. Assumptions for tracking control and dynamic regulation of the MTN controller for nonlinear time-varying delay systems with two degrees-freedom design methods are obtained by the above proof. The relationship between system response and controller parameters is also demonstrated by the above proof. And a convenient design procedure of the MTN controller is given. Tracking control and dynamic regulation for nonlinear time-varying delay systems by a CSTR and a numerical example are illustrated. Based on above numerical example, the problem of tracking control and dynamic regulation of MIMO nonlinear time-varying delay systems by the MTN controller also has been briefly discussed.
学术讨论
主办单位时间地点报告人报告主题
东南大学自动化学院 2017.09 中心楼二楼教育部重点实验室会议室 忻欣 教授 Reduced-Order Stable Controllers for Underactuated Planar Robots
东南大学自动化学院 2016.09 中心楼二楼教育部重点实验室会议室 冯有翼 教授 Optimal Complementary Analysis of an Assemble-to-Order System with Serial W Structure
东南大学自动化学院 2015.04 中心楼二楼教育部重点实验室会议室 陈文华 教授 Robust Control of Uncertain Nonlinear Systems: A Nonlinear DOBC Approach
东南大学自动化学院 2015.04 中心楼二楼教育部重点实验室会议室 夏元清 教授 自抗扰在典型工业过程中的应用
制造系统控制与优化研究所 2015.01 中心楼636会议室 康安明 基于离散多维泰勒网的SISO非线性系统稳定性分析和动态调节
制造系统控制与优化研究所 2016.01 中心楼636会议室 康安明 非线性时变时滞系统多维泰勒网控制的稳定性分析与动态性能调节
制造系统控制与优化研究所 2016.06 中心楼636会议室 康安明 基于多维泰勒网控制的执行器饱和多入多出非仿射非线性系统跟踪控制与动态调节
制造系统控制与优化研究所 2016.11 中心楼636会议室 康安明 考虑执行器饱和的时变时滞非线性系统多维泰勒网跟踪控制与动态调节
     
学术会议
会议名称时间地点本人报告本人报告题目
15th International Conference on Control, Automation and Systems 2015.10 Busan, Korea Asymptotically Tracking and Dynamic Regulation of SISO Nonlinear System Based on Multi-dimensional Taylor Network Controller
非线性系统的多维泰勒网控制控制 2015.01 南京,中国 基于离散多维泰勒网的SISO非线性系统稳定性分析和动态调节
     
代表作
论文名称
Asymptotically tracking and dynamic regulation of SISO nonlinear system based on multi-dimensional T
Stability analysis and dynamic regulation of multi-dimensional Taylor network controller for SISO no
 
答辩委员会组成信息
姓名职称导师类别工作单位是否主席备注
徐胜元 正高 教授 博导 南京理工大学
叶文华 正高 教授 博导 南京航空航天大学
费树岷 正高 教授 博导 东南大学
孙长银 正高 教授 博导 东南大学
李世华 正高 教授 博导 东南大学
      
答辩秘书信息
姓名职称工作单位备注
邵家玉 副高 副教授 东南大学